Peak locations are biased in under-resolved cases, both
in amplitude and frequency

The preceding figures suggest that, for a rectangular window of length
, two sinusoids can be most reliably resolved when they are
separated in frequency by a full main-lobe width:

This implies there must be at least two full cycles of the
difference-frequency under the window. (We'll see later that this is
an overly conservative requirement--a more careful study reveals that
cycles is sufficient for the rectangular window.)

In principle, arbitrarily small frequency separations can be resolved if

we are sure we are looking at the sum of two ideal sinusoids under the window.

However, in practice, there is almost always some noise and/or
interference, so we prefer to require sinusoidal frequency separation
by at least one main-lobe width (of the sinc-function in this case, or
the window transform more generally) whenever possible.

The rectangular window provides an abrupt transition at its edge. We
will soon look at some other windows which have a more gradual
transition. This is usually done to reduce the height of the side
lobes.